techniques
Three-and-a-half ways around a Moebius loop
or, How to Knit a Moebius Loop
or, How to Knit a Möbius or Mobius strip, band, or loop
There are four parts:
- Introduction and the topological classification of knitting (this page)
- The "transverse" method
- The "inside-out" (or provisional cast-on) method: two variants
- The "outside-in" method
Introduction and the topological classification of knitting
A Moebius loop (named after August Ferdinand Möbius, the most common alternate spellings are "Mobius", and "Moebius"; conventionally, if you choose to drop the umlaut over the "o", you add an "e"), as you probably know, is a topological phenomenon consisting of a single surface and a single boundary edge that we can realize in three-dimensional knitting.
And they're fun to play with.
Most things that are knit have two surfaces: an inside and an outside, or a public side and a private side, or front and back, or however you'd like to label them. Some knitted items have one boundary edge; some have two or more.
A simple scarf, hat, or sock has a single boundary edge, but it has two surfaces: in a scarf, you'd call these surfaces "front" and "back", and in a hat or sock, "inside" and "outside". If you get a hole in your sock, you'll have two boundary edges.
A simple headband, which is shaped like a cylinder, has two boundary edges and two surfaces.
But the Moebius loop, while it seems loopy like a headband, only has one boundary edge and one surface. You can recreate this phenomenon by cutting a strip of paper that is significantly longer than it is wide, giving one end a half-twist, then taping the ends together to form a loop. Try drawing a line down the middle of one "side" of the loop -- you'll discover that there is only one side, now, although you had started with a piece of paper with two sides! (In a sense, this is a "cheating" way of making a moebius loop, because there is a seam where you taped the paper together. More on "cheating" later.)
Why?
Making knitted versions of a Moebius loop is somewhat akin to a party trick, but many people extoll its virtues: for example, if you make a neckwarmer that is a Moebius loop and place the half-twist at centre front, the neckwarmer will snug up against your neck, but it will also lie flat against your chest and not add bulk under your coat, the way a conventionally tied scarf would. Madeleine Vionnet, the French designer reknown for her use of bias-cut designs, created the Moebius scarf in the early part of the 20th century. But rather than wearing the Moebius loop as a neck ring, as most knit Moebius scarves are worn today, Vionnet draped her scarf over the back of the neck, with the two U-ends of the loop hanging down the front. Each U-end was then pulled inside the other (the fun way is to cross your arms, grasp one U-end in each hand, then uncross your arms)
I'm also pretty certain that in my high school, the washrooms were supplied with cloth towels that were in fact long strips of dishtowelling sewed in a Moebius loop: a length of towelling hung in a "U" from a spool fitted with some kind of ratchet and detent system that allowed a wipe's worth of towel to be pulled downward at the front of the U, while the spool wound up an equivalent amount from the back of the U. The reason I think it was a Moebius is because initially, the users would soil the outer face of the towel U, but eventually you'd see the same marks on the inner face of the U. Perhaps this was intended to fool us into thinking it was hygenic. But enough reminiscing about high school washrooms.
How?
In knitting, there are three general construction methods for a Moebius loop:
The easiest method involves seaming a long strip of knitting to form a loop. It can be worked with straight or circular needles. Because each method of loop construction involves something that can be equated with a seam, we'll call this method the transverse method because it requires a join that is perpendicular to the boundary edge. Click here to read about the transverse method.
The next-easiest method involves working the Moebius loop from the inside-out, and requires circular needles. Typically it employs a provisional (or provisional-like) cast-on and knitting into the top and bottom of the first row, so that one may work from the middle of the moebius loop outward. The first few rows are difficult to work because the stitches need to be urged gently along a contorted circular needle, but it gets easier as the work progresses. Click here to read about the inside-out method. There are actually two variants to this technique: one uses waste yarn, and the other doesn't. So together, they're one and a half methods.
The final method constructs the Moebius loop from the outside-in and is based on what you get when you cut a moebius loop down the middle. (Don't know? Get yourself paper, tape, and scissors, and try it out.) It might be considered the most challenging -- but only if you don't like grafting or seaming, because the actual knitting is easier than the inside-out method. Like the inside-out method, the outside-in method requires circular needles, too, because you must knit a large loop that's twice the size of your finished Moebius loop. Click here to read about the outside-in method.
Conclusion
As you can see from comparing the advantages and disadvantages of these techniques, all of these methods have inherent flaws, either in the difficulty of construction or in the fact that the initial cast-on or final grafting gives away the construction method. It can't be helped. Moebius loops can be manufactured as truly seamless, glitchless articles (like my vacuum cleaner drive belt, for example). It's just not within the realm of two sticks and string, because we're knitting with a finite length of yarn and our knitting must have a beginning and an end. This goes for both the inside-out and the outside-in methods. If we wanted to make a Moebius loop with perfect integrity, we'd be working with clay, or metal, or something like that. (While you could weave a Moebius loop, you'd either have to deal with the two ends of the warp, or set up a warp as a series of loops, which means you'd have to splice your warp yarn to make a series of loops. And of course your weft has a finite length, as well.)
While I&P suggest that the seamed method of construction is not ideal, with careful finishing the final result is just about as seamless as the ...